(i)[3]
Using the perpendicular distances of $D$ and $E$ from $AB$, show that the exact value of $\theta$ is $\sin^{-1}\left(\frac{3\sqrt{3}}{10}\right)$.
(ii)[5]
Find the perimeter of the shaded region, correct to 4 significant figures.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The diagram depicts circle $C_1$ touching circle $C_2$ at point $X$. Circle $C_1$ is centred at $A$ and has radius $6\text{ cm}$, whereas circle $C_2$ is centred at $B$ and has radius $10\text{ cm}$. Points $D$ and $E$ are on $C_1$ and $C_2$ respectively, and $DE$ is parallel to $AB$. Angle $DAX = \frac{\pi}{3}$ radians and angle $EBX = \theta$ radians.